Hierarchical Decomposition of Large-Variable Boolean Functions Using Recursive Fundamental-Block Minimization

We present a hierarchical decomposition architecture for Boolean
function minimization that extends single-output structural-atom
recognition from a base engine of K input variables (typically
K=4) to arbitrarily large N (16, 32, 64, 128+). The architecture
partitions an N-variable specification into 2^(N-K) cofactor
sub-specifications indexed by the upper N-K variables; identifies
equivalence classes of cofactors that share the same minterm set;
invokes the K-variable base engine once per unique cofactor;
constructs a selector function over the upper variables for each
cofactor group; recursively minimizes each selector function by
the same architecture; and composes the result as a sum of
products selector * cofactor. Verification of the composed
expression against the original specification ensures
correctness. The architecture is intrinsically parallelizable:
the 2^(N-K) cofactor minimizations are independent. Tested at
N=8 and N=16 with single-recursion-level decomposition and a
4-variable base engine. The architecture extends to N=32, 64,
and 128 by additional recursion levels with computational cost
that grows polynomially in the number of unique cofactor groups
rather than exponentially in N. Companion to the foundational
M-Maps paper (DOI 10.5281/zenodo.20498821) and the structural-
atom engine paper (DOI 10.5281/zenodo.20499264).